” Holding the dead-battery fob right next to the push button might work as well. “
Since Lexus and Ford say that is the only way, it had better work!
“Also, these keyless fobs have an insert on the dashboard - usually to the left or right of the steering column - where you can insert the fob and start the car, should the battery on the fob be dead.”
Just reread your post. That is the same as I described. Just where the sensor is located. Special slot, on the button or in the console.